-54=-8x-5x^2

Solution for -54=-8x-5x^2 equation:

-54=-8x-5x^2

We move all terms to the left:

-54-(-8x-5x^2)=0

We get rid of parentheses

5x^2+8x-54=0

a = 5; b = 8; c = -54;
Δ = b2-4ac
Δ = 82-4·5·(-54)
Δ = 1144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1144}=\sqrt{4*286}=\sqrt{4}*\sqrt{286}=2\sqrt{286}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-2\sqrt{286}}{2*5}=\frac{-8-2\sqrt{286}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+2\sqrt{286}}{2*5}=\frac{-8+2\sqrt{286}}{10}
$